Distributed Adaptive Accelerated Nash Equilibrium Seeking for Noncooperative Games: A Differentially Private Method

This article is concerned with a distributed algorithm for seeking the Nash equilibrium in noncooperative games with partial-decision information, which simultaneously addresses the protection of individual privacy and ensures fast algorithmic convergence. First, a differential privacy mechanism is used in the fully distributed consensus-based projected pseudo-gradient algorithm to obfuscate shared messages over the communication network and quantify the algorithm’s privacy level. To achieve fast convergence, a novel relaxed inertial method is designed, consisting of two steps with independently designed parameters: 1) a relaxation step and 2) an inertia step. The adaptive inertia coefficient in the inertia step is designed based on the iteration error of the players’ estimated decisions and a decaying sequence, with the only requirement being the non-negativity of its internal parameters. Compared to existing approaches, our algorithm exhibits high flexibility in parameter selection. Furthermore, we analyze the algorithm’s convergence and differential privacy under both linearly decaying and fixed stepsizes within a unified framework, providing sufficient conditions that are independent of the number of players. Finally, numerical simulations validate the algorithm’s potential, demonstrating significant improvements in convergence rate, accuracy, and privacy level.